Elastic full wavefield inversion with refined anisotropy and vp/vs models

ABSTRACT

Methods for inversion of seismic data to infer subsurface physical property parameters, comprising constructing an inhomogeneous anisotropy model and/or inhomogeneous V S /V P  or V P /V S  model; and inverting the seismic data in a sequential or simultaneous approach to obtain at least one subsurface physical property parameter using an elastic inversion algorithm and the inhomogeneous anisotropy model and/or inhomogeneous V S /V P  or V P /V S  model. Constructing an inhomogeneous anisotropy model may comprise deriving geobodies from at least one of seismic facies analysis, regional geologic information, or seismically derived earth models; and adjusting at least one of ε, δ, γ, or parameters of the elastic stiffness tensor matrix in a homogeneous anisotropy model in areas corresponding to the geobodies. Constructing an inhomogeneous V S /V P  or V P /V S  model may comprise deriving geobodies and adjusting values in a homogeneous V S /V P  or V P /V S  model in areas corresponding to the geobodies.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication 62/751,095 filed Oct. 26, 2018 entitled ELASTIC FULLWAVEFIELD INVERSION WITH REFINED ANISOTROPY AND VP/VS MODELS, theentirety of which is incorporated by reference herein.

TECHNOLOGICAL FIELD

The present disclosure relates to the field of geophysical prospecting,including to prospecting for hydrocarbons, and more particularly, toseismic data processing. Specifically, aspects of the present disclosurerelate to methods for seismic data inversion that incorporate aninhomogeneous anisotropy model.

BACKGROUND

This section is intended to introduce various aspects of the art, whichmay be associated with the present disclosure. This discussion isintended to provide a framework to facilitate a better understanding ofparticular aspects of the present disclosure. Accordingly, it should beunderstood that this section should be read in this light, and notnecessarily as an admission of prior art.

An elastic earth model is typically parameterized by compressional wavevelocity (V_(P)), shear wave velocity (V_(S)), and density (ρ), inaddition to anisotropic parameters and attenuation of the medium.Anisotropic parameters are commonly referred to as Thomsen'sparameters—δ (delta), ϵ (epsilon), and γ (gamma)—which respectivelyreflect near-offset effects, long-offset effects, and S-wave effects.

Extracting earth model parameters from seismic data is commonly referredto as seismic inversion. One of the most commonly used approaches forinverting for earth parameters is linear inversion (e.g., Hampson(2012), Minkoff (1995), Routh (2006), Downton (2011)). In most of theseimplementations, the data is imaged using a kinematic model comprisingvelocity and anisotropy to generate image gathers or angle dependentstacks. Band-limited elastic properties are then inverted from the imagegathers (commonly referred to as pre-stack AVO inversion) or from angledependent stacks (also known as post-stack AVO inversion). A key aspectof these types of inversion is that the mapping of the band-limitedelastic parameters to the amplitude part of the data is linear and,therefore, very tractable computationally. Since these methods areapplied to post-imaged data, the errors from imaging need to beaccounted for and/or data need to be conditioned to make the resultsmeaningful. Nonetheless, these methods may produce acceptable resultsfor parameters that are more sensitive to the near to conventional faroffset (i.e., angle of incidence between 5° and 45°), such asP-impedance (I_(P)), S-impedance (I_(S)), and V_(P)/V_(S) ratio. It maybe challenging, however, for pre-stack and post-stack inversion schemesto provide reliable results with respect to a third parameter such asP-wave velocity (V_(P)) and density (ρ).

Due to computational advances and the ability to solve for the full waveequation (Aki (1980)), inversion for earth parameters has been proposedusing Full Waveform Inversion (“FWI”) (e.g., Tarantola (1984), Tarantola(1988), Sears (2008), Virieux (2009), Krebs (2009), Baumstein (2011),Routh (2014), Krebs (2016)). FWI is an approach to seismic data analysisand imaging that seeks to model earth parameters using amplitude andphase information from seismic waveforms, not only travel times astomography and migration techniques. Specifically, FWI estimates avelocity model, or earth model in general, by minimizing the phase andamplitude mismatch between simulated and observed data. For example, atypical FWI algorithm may be generally described as follows: using astarting subsurface physical property model, synthetic seismic data aregenerated, i.e. modeled or simulated, by solving a wave equation using anumerical scheme (e.g., finite-difference, finite-element, etc.). Thesynthetic data are compared with the observed seismic data and using thedifference between the two, an error or objective function is calculated(the objective function is a measure of the misfit between the simulatedand observed data). Using the objective function, a modified subsurfacemodel is generated which is used to simulate a new set of syntheticseismic data. This new set of synthetic seismic data is compared to thefield data to generate a new objective function. This process isrepeated until the objective function is satisfactorily minimized andthe final subsurface model is generated. Earth parameters may bereconstructed individually by single-parameter FWI or simultaneously bymulti-parameter FWI.

A global or local optimization method may be used to minimize theobjective function and to update the subsurface model. For example, alocal cost function optimization procedure for FWI may involve: (1)selecting a starting model; (2) computing a search direction; and (3)searching for an updated model that is a perturbation of the model inthe search direction. The cost function optimization procedure may beiterated by using the new updated model as the starting model forfinding another search direction, which may then be used to perturb themodel in order to better explain the observed data. The process maycontinue until an updated model is found that satisfactorily explainsthe observed data. Commonly used local cost function optimizationmethods include gradient search, conjugate gradients, quasi Newton,Gauss-Newton and Newton's method. Commonly used global methods includeMonte Carlo, simulated annealing, genetic algorithms, evolutionaryalgorithms, particle based optimization, or grid search.

The most common form of the wave equation used in FWI is the variabledensity acoustic wave equation, which assumes no S-waves. Acoustic FWImay be appropriate in many cases because it is usually sufficient toconsider only P-wave propagation to save processing time. In suchscenarios, modeling of wave propagation depends only on density ρ andV_(P), as it is well known that PP reflection (P-wave down/P-wave up) atnormal incident angle is largely determined by the acoustic impedanceI_(P)=ρV_(P). However, acoustic impedance I_(P) alone is not always agood indicator of reservoir rocks and types because fluid types can bebetter retrieved from elastic parameters such as V_(P)/V_(S). As aresult, multi-parameter elastic FWI approaches to invert for I_(P) andV_(P)/V_(S) have been proposed. For example, Wang et al. (2017) proposean approach that decomposes data into offset or angle groups andperforms elastic FWI on them in sequential order. Their approachutilizes the relationship between reflection energy and reflectionangle, or equivalently, offset dependence in elastic FWI. For example,their approach may be implemented by extracting only PP-mode data fromseismic data, and inverting the PP-mode data sequentially in two or moredifferent offset ranges, each offset range inversion determining atleast one physical property parameter, wherein in a second andsubsequent inversions, parameters determined in a previous inversion areheld fixed. Physical parameters include, but are not limited to, V_(P),V_(S), and ρ.

The ability to simulate elastic waves in the subsurface and match theseismic data at near, mid, far, and ultra-far (i.e., beyond 45°) offsetsprovides the opportunity to extract more detailed subsurface properties.However, the amplitude of the data at far and ultra-far offsets not onlydepends on the elastic parameters of the medium, but also on anisotropyand attenuation. Unfortunately, existing elastic FWI approaches rely onconventional anisotropy models obtained from imaging that are typicallylow-frequency (spatially smooth) and do not show inhomogeneousvariations in anisotropy such as layer to layer contrasts or geobodycontrasts. Consequently, the inverted V_(P) results tend to becontaminated by anisotropy effects. The need exists, therefore, for anapproach that effectively takes into account crosstalk between V_(P) andanisotropy in elastic FWI in order to fit the amplitude data at largeoffsets.

SUMMARY

The present disclosure provides methods for incorporating aninhomogeneous anisotropy model in seismic inversion. In someembodiments, the inhomogeneous anisotropy model may be incorporated inelastic FWI to improve the stability and accuracy of inversion for athird parameter such as V_(P) and/or ρ. Alternatively, the inhomogeneousanisotropy model may be used to invert for multiple parameterssimultaneously.

The present disclosure also provides computer-implemented methods forinversion of seismic data to infer subsurface physical propertyparameters, including any one of P-wave velocity V_(P), S-wave velocityV_(S), density, lambda, mu, and combinations thereof. One methodcomprises constructing an inhomogeneous anisotropy model; and invertingthe seismic data in a sequential or simultaneous approach to obtain atleast one subsurface physical property parameter using an elasticinversion algorithm and the inhomogeneous anisotropy model. Anothermethod comprises constructing an inhomogeneous anisotropy model and aninhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model; and inverting theseismic data in a sequential or simultaneous approach to obtain at leastone subsurface physical property parameter using an elastic inversionalgorithm and the inhomogeneous anisotropy model and the inhomogeneousV_(S)/V_(P) or V_(P)/V_(S) model. A third method comprises constructingan inhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model; and inverting theseismic data in a sequential or simultaneous approach to obtain at leastone subsurface physical property parameter using an elastic inversionalgorithm and the inhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model.

Constructing an inhomogeneous anisotropy model may comprise derivinggeobodies from at least one of seismic facies analysis, regionalgeologic information, or seismically derived earth models; and adjustingat least one of ε, δ, γ, or parameters of the elastic stiffness tensormatrix in a homogeneous anisotropy model in areas corresponding to thegeobodies. For example, where the geobodies are sand geobodies, ε and δmay be adjusted to be less than or equal to zero. Constructing aninhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model may comprise derivinggeobodies from at least one of seismic facies analysis, regionalgeologic information, or seismically derived earth models; and adjustingvalues in a homogeneous V_(S)/V_(P) or V_(P)/V_(S) model in areascorresponding to the geobodies. For example, where the geobodies aresand geobodies, areas corresponding to sand may be assigned lowerV_(P)/V_(S) values if constructing a V_(P)/V_(S) model, or assignedhigher V_(S)/V_(P) values if constructing a V_(S)/V_(P) model.

According to certain aspects of the present disclosure, using an elasticinversion algorithm may comprise extracting only PP mode data from theseismic data; inverting the PP mode data sequentially in two or moredifferent offset ranges, each offset range inversion determining P-waveimpedance (I_(P)) and at least one of S-wave impedance (I_(S)), P-wavevelocity over S-wave velocity (V_(P)/V_(S)), S-wave velocity over P-wavevelocity (V_(S)/V_(P)), and S-wave velocity (V_(S)), wherein in a secondand subsequent inversions, parameters determined in a previous inversionare held fixed; and using the inverted subsurface physical propertyparameters to construct the inhomogeneous anisotropy model. In someembodiments, a near-offset range may be sequentially first to beinverted to infer I_(P), using a computer programmed with an acoustic orelastic inversion algorithm. A mid-offset range may be sequentiallysecond to be inverted to infer at least one of I_(S), V_(P)/V_(S),V_(S)/V_(P), and V_(S), with I_(P) fixed at its value from the firstinversion, said second inversion using an elastic inversion algorithm.Inverting the seismic data may be performed in a sequential approachcomprising inverting a far-offset range to infer density or V_(P), usingan elastic inversion algorithm, with I_(P) fixed at its value from theinversion of the near-offset range and I_(P) or V_(P)/V_(S) orV_(S)/V_(P) or V_(S) fixed at its value from the inversion of themid-offset range. The inversions of the near-offset data, mid-offsetdata, and far-offset data may be repeated at least one time to updatethe inferred physical property parameters. In some embodiments, theacoustic and elastic inversion algorithms are full waveform inversionalgorithms.

The foregoing has broadly outlined the features of the presentdisclosure so that the detailed description that follows may be betterunderstood. Additional features will also be described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects and advantages of the disclosure willbecome apparent from the following description, appending claims and theaccompanying drawings, which are briefly described below.

FIG. 1 is an exemplary chart showing the anisotropy effect on AVA.

FIG. 2 is a flow chart showing basic steps of one embodiment of seismicdata processing methods according to the present disclosure.

FIG. 3A is an exemplary I_(P) model; FIG. 3B is an exemplary V_(S)/V_(P)model; FIG. 3C is an exemplary conventional (smooth) anisotropy model;FIG. 3D is an exemplary inhomogeneous anisotropy model modifiedaccording to aspects of the present disclosure; FIG. 3E is the “true”anisotropy model; FIG. 3F is the V_(P) model obtained with elastic FWIusing the conventional anisotropy model; FIG. 3G is the V_(P) modelobtained with elastic FWI using the inhomogeneous anisotropy model; andFIG. 3H is the inverted true V_(P) model.

FIG. 4 is an exemplary well log comparison of V_(P) obtained with andwithout using a modified, inhomogeneous anisotropy model according toaspects of the present disclosure.

FIG. 5 is a flow chart showing basic steps in another embodiment ofseismic processing methods according to the present disclosure.

FIG. 6A is an exemplary conventional V_(S)/V_(P) model; FIG. 6B is anexemplary inhomogeneous V_(S)/V_(P) modified according to aspects of thepresent disclosure; FIG. 6C is the “true” V_(S)/V_(P) model; FIG. 6D isthe inverted V_(S)/V_(P) model obtained with elastic FWI using theconventional (smooth) V_(S)/V_(P) model; FIG. 6E is the invertedV_(S)/V_(P) model obtained with elastic FWI using the inhomogeneousV_(S)/V_(P) model and an inhomogeneous anisotropy model (not shown); andFIG. 6F is the inverted true V_(S)/V_(P) model.

FIG. 7 is an exemplary well log comparison of V_(S)/V_(P) obtained withand without using a modified, inhomogeneous V_(S)/V_(P) model accordingto aspects of the present disclosure.

FIG. 8 is a flow chart showing basic steps in another embodiment ofseismic processing methods according to the present disclosure.

FIG. 9 is a diagram of an exemplary computer system that may be utilizedto implement aspects of the present disclosure.

It should be noted that the figures are merely examples and nolimitations on the scope of the present disclosure are intended thereby.Further, the figures are generally not drawn to scale, but are draftedfor purposes of convenience and clarity in illustrating various aspectsof the disclosure. Certain features and components therein may be shownexaggerated in scale or in schematic form and some details ofconventional elements may not be shown in the interest of clarity andconciseness. When describing a figure, the same reference numerals maybe referenced in multiple figures for the sake of simplicity.

DETAILED DESCRIPTION

To promote an understanding of the principles of the disclosure,reference will now be made to the features illustrated in the drawingsand no limitation of the scope of the disclosure is hereby intended byspecific language. Any alterations and further modifications, and anyfurther applications of the principles of the disclosure as describedherein are contemplated as would normally occur to one skilled in theart to which the disclosure relates.

The amplitude of seismic data at far and ultra-far offsets not onlydepends on the elastic parameters of the medium, but also on anisotropyand attenuation. To illustrate the significance of anisotropy effects,reference is made to FIG. 1, which shows the Amplitude Versus Angle(AVA) response at the top of an exemplary class 2P oil reservoir. Inparticular, reflectivity is plotted against Angle of Incidence, withcurve 102 corresponding to the AVA response in the case of ananisotropic shale (ε=0.12, δ=0.06)/isotropic sand interface and curve104 corresponding to the AVA response in the case of an isotropic shale(ε=δ=0)/isotropic sand interface. It can be appreciated from FIG. 1 thatthe difference between anisotropic and isotropic cases is negligiblebelow about 30°, but very significant beyond about 40°. However theslope and intercept of the AVA below 30° are only controlled by contrastin I_(P) and V_(P)/V_(S) ratio; there is no effect of V_(P) contrastalone. Also shown are the intercept-gradient 2-term approximations ofcurves 102 and 104, respectively, as lines 106 and 108. The curvaturedifference between 106 and 102 or 108 and 104 is controlled by the V_(P)contrast between sand and shale. The curvature effect is only noticeablefor angles beyond about 45°-50°. The critical angle (i.e., the angle atwhich the wavefield changes from reflection to refraction) for theanisotropic and isotropic curves is shown at 110 and 112, respectively.The value of the critical angle is also controlled by the V_(P) contrastbetween shale and sand. Therefore, it is evident that, to obtainaccurate inversion results for parameters such as V_(P), one must usedata corresponding to angle beyond 45° where the anisotropy contrastshould not be neglected.

Aspects of the technological advancement described herein incorporatehigher resolution anisotropy in seismic inversion, particularly elasticFWI, to take into account non-smooth anisotropy variations in thesubsurface. Benefits of the disclosed approaches include the ability toobtain improved physical property models by decoupling the effects ofanisotropy in the amplitude component of the seismic data. In thiscontext, the terms velocity model, earth model, or physical propertymodel refer to an array of numbers, typically a three-dimensional array,where each number, which may be called a model parameter, is a value ofvelocity or another physical property in a cell, and where a subsurfaceformation has been conceptually divided into discrete cells forcomputational purposes. Non-limiting examples of such physicalproperties or model parameters include P-wave impedance I_(P), S-waveimpedance I_(S), P-wave velocity V_(P), S-wave velocity V_(S), P-wavevelocity divided by S-wave velocity (V_(P)/V_(S)), S-wave velocitydivided by P-wave velocity (V_(S)/V_(P)), density ρ, λ (lambda), and μ(mu).

According to some aspects of the present disclosure, an inhomogeneousanisotropy model may be constructed based on interval anisotropyvariations or anisotropy contrasts in the subsurface, such as geobodies.Specifically, in some embodiments, three-dimensional sand geobodies maybe used to update conventional low-frequency imaging anisotropy models.Sand geobodies may in turn be constructed using seismic facies analysis,regional geologic knowledge, or seismically derived earth models such asI_(P) and V_(P)/V_(S) (or V_(S)/V_(P)) or Volume-of-Shale cubes. Forexample, it is known that sand layers are much more isotropic (ε andδ≤0) than background shale (c may range from 0.05 to 0.3). However, theanisotropy of the earth has much less influence on the seismic data atlower angles. Therefore, according to some aspects of the presentdisclosure, V_(P)/V_(S) and I_(P) volumes may be derived from elasticFWI or conventional migration and used to guide the construction of thesand geobodies directly or in conjunction with the regional geologicalinformation, any available seismic facies information, and horizoninterpretation.

Having constructed sand geobodies, low-frequency imaging anisotropymodels may then be updated by adjusting the value of at least one of ε,δ, γ, or parameters of the elastic stiffness tensor matrix in ananisotropy model in areas corresponding to the geobodies. For example, εand δ may be set to ε≤0 and δ≤0 (and optionally γ may also be set toγ≤0) in areas corresponding to the sand geobodies, thereby obtaininghigher-resolution anisotropy cubes. The low-frequency anisotropy modelsmay be obtained by any method known in the art (e.g., anisotropytomography, or conventional velocity analysis to generate anisotropymodels to flatten gathers). The higher resolution anisotropy model maycorrespond to sand, carbonate, or other lithology whose anisotropy isdifferent from the background. A high-cut filter may be optionallyapplied to the resulting cubes to avoid sharp edge effects. In thisregard, a 6 Hz high-cut may be sufficient, but cuts at higherfrequencies may be required for higher frequency elastic FWI (thehigh-cut frequency preferably should be the maximum frequency expectedto be retrieved by the elastic FWI).

The inhomogeneous anisotropy model may then be incorporated into seismicdata inversion, including according to some embodiments described below.For example, the derived anisotropy model may be used in the elastic FWIsimulation to explain the data typically at the far and ultra-faroffsets. It should be understood that, while some exemplary workflowsare described below, it is contemplated that an inhomogeneous anisotropymodel may be incorporated into single-parameter and multi-parameterinversion schemes, including acoustic and elastic FWI, as appropriate.

With reference to FIG. 2, a flow chart is provided showing basic stepsin one embodiment of methods of the present disclosure. Specifically, atstep 202, the method may begin by inverting seismic data to infer P-waveimpedance (I_(P)) and at least one of S-wave impedance (I_(S)), P-wavevelocity over S-wave velocity (V_(P)/V_(S)), S-wave velocity over P-wavevelocity (V_(S)/V_(P)), and S-wave velocity (V_(S)). This may be doneusing conventional migration or elastic FWI. For example, one elasticFWI sequential approach may involve extracting only PP mode data fromthe seismic data. The PP mode data may be inverted sequentially in twoor more different offset ranges, each offset range inversion determiningat least one physical property parameter, wherein in a second andsubsequent inversions, parameters determined in a previous inversion areheld fixed. For instance, the PP mode data may be divided intonear-offset range, a mid-offset range, and a far-offset range, whichranges may or may not overlap. The near-offset data may be invertedusing an acoustic inversion algorithm to obtain a first parameter (e.g.,I_(P)), and the mid-offset data may be inverted using an elasticinversion algorithm to obtain a second parameter (e.g., V_(P)/V_(S)),with the first parameter held fixed from the previous step. In certainembodiments, the near-offset range might be <500 m with the far-offsetrange being >2 km, and the mid-offset range being in between.

At step 204, an inhomogeneous anisotropy model may be constructed usingthe physical parameters derived in step 202 (e.g., I_(P) and V_(P)/V_(S)volumes obtained from near-offset and mid-offset data using elasticFWI). It should be understood, however, that this is only one possibleembodiment and the present disclosure contemplates embodiments in whichstep 202 is omitted and an anisotropy model is constructed on the basisof seismic facies analysis or regional geologic knowledge alone, forexample.

Next, at step 206, the inhomogeneous anisotropy model may beincorporated into elastic FWI inversion as described above to infer oneor more earth model parameters. For example, in embodiments where afirst and second parameter have been previously obtained (e.g., I_(P)and V_(P)/V_(S)) to use in constructing the anisotropy model, thesequential elastic FWI approach may continue to invert the far-offsetrange of seismic data, using an elastic inversion algorithm, for a thirdparameter, which can be any of V_(P), V_(S), V_(P)/V_(S), V_(S)/V_(P),density ρ, λ (lambda), μ (mu), with any parameters obtained previouslyheld fixed. For instance, the far-offset range may be inverted for V_(P)or density ρ with I_(P) and V_(P)/V_(S) fixed. If one of V_(P) ordensity ρ is obtained, the other may be computed using I_(P) and thedefinition of acoustic impedance I_(P)=ρV_(P). Similarly, if one ofV_(s) or density ρ is obtained, the other may be computed using I_(s)and the definition of acoustic impedance I_(S)=ρV_(S). Model parametersmay also be continuously updated using the following equations:

$\begin{matrix}{\frac{\rho_{updated}}{\rho_{model}} = {\frac{I_{P\mspace{14mu} {updated}}}{I_{P\mspace{14mu} {model}}} - \frac{V_{P\mspace{14mu} {updated}}}{V_{P\mspace{14mu} {model}}}}} & (1) \\{\frac{\rho_{updated}}{\rho_{model}} = {\frac{I_{S\mspace{14mu} {updated}}}{I_{S\mspace{14mu} {model}}} - \frac{V_{S\mspace{14mu} {updated}}}{V_{S\mspace{14mu} {model}}}}} & (2)\end{matrix}$

Alternatively, at step 206, multi-parameter inversion may be performedsimultaneously using elastic FWI. (See e.g., Wang et al. (2017); Sears(2008); Prieux (2013); Mora (1988); Operto (2013)).

Optionally, during iterations to invert for a third parameter or performsimultaneous inversion of multiple parameters in step 206 incorporatingthe inhomogeneous anisotropy model, the anisotropy model may also beused to check image gathers and adjust if the gather alignment degrades.Specifically, the kinematic information in the far and ultra-far offsetdata is strongly dependent on the P-wave velocity and anisotropy of thesubsurface. Accordingly, the alignment of the image gathers obtained viamigration with the higher resolution anisotropy model may provide acheck on the integrity of the kinematic information, for example. Thismay be particularly necessary if sand geobodies are relatively thick(i.e., >100 m).

With reference to FIGS. 3A-3H, an example is provided to demonstratesome advantages of the method described in FIG. 2. Synthetic (computersimulated) data was used in this test example to demonstrate aspects ofthe technological advancement described herein. The simulation of thedata was carried out using full elastic wave physics where the elasticparameters of the subsurface such as V_(P), V_(S), density andanisotropy are input to generate the synthetic data. Full elasticsynthetic data were created as shots and used for inversion tests. TheI_(P) and V_(S)/V_(P) models obtained by inverting PP data up to 45°offset angles in a sequential FWI approach are shown in FIG. 3A and FIG.3B, respectively. Specifically, near-offset data was inverted to obtainI_(P) using an acoustic wave equation; I_(P) was then held constant toinvert mid-offset data to obtain V_(S)/V_(P). Several iterations in theorder of tens may be needed to obtain a good fit to the shot data andestimate V_(S)/V_(P) model. Also, initial V_(P) and density models areneeded to perform acoustic FWI. The initial V_(P) model can be derivedfrom traditional migration velocity analysis, and for this synthetictest, a smoothed version of the “true” V_(P) profile (used to forwardmodel the synthetic data) was used. The initial density model can bederived from the empirical relationship between density and V_(P). Forsimplicity, a constant density (e.g. 1000 kg/m³) model can also be used.

A conventional low-frequency imaging anisotropy model is shown in FIG.3C which, as can be appreciated, is relatively smooth. Using theV_(S)/V_(P) model as a shale indicator, the anisotropy model was updatedto construct an inhomogeneous anisotropy model as shown in FIG. 3D. Forcomparison, FIG. 3E shows the true anisotropy mode, which was generatedbased on the synthetic data.

Next, two V_(P) models are presented in FIG. 3F and FIG. 3G, bothgenerated through elastic FWI, maintaining the I_(P) and V_(S)/V_(P)models fixed. FIG. 3F shows V_(P) inverted using the “smooth” anisotropymodel of FIG. 3C, while FIG. 3G shows V_(P) inverted using the modified,inhomogeneous anisotropy model of FIG. 3D. The “true” V_(P) profile usedto generate the synthetic data is provided in FIG. 3H. It can beappreciated that the V_(P) model obtained using an inhomogeneousanisotropy (FIG. 3G) model exhibits better resolution and is much closerto the true V_(P) profile of FIG. 3H than the V_(P) model generatedusing a conventional (smooth) anisotropy model (FIG. 3F).

In particular, improved magnitude and conformance to structure can beobtained in the class 2/2P areas (below 2,500 m). For example, FIG. 4shows a well log comparison of V_(P) obtained with and without using amodified, inhomogeneous anisotropy model according to aspects of thepresent disclosure, at the location of a class 2P reservoir. Line 402corresponds to the conventional (unmodified) c model, line 404 to the cmodel updated as described herein (inhomogeneous anisotropy), and line406 to the “true” c model. Corresponding inverted V_(P) models (afterdetrending) 412, 414, and 416 were generated using the conventional cmodel, modified c model, and the true c model, respectively. The curve416 represents the true V_(P) property, which must be predicted asaccurately as possible to obtain reliable reservoir characterization. Itcan be appreciated that the detrended V_(P) model 412 using theconventional anisotropy model under-predicts the reservoir V_(P)magnitude and over-predicts the V_(P) magnitude in the shale above andbelow, curve 416. However, the detrended V_(P) curve 414 resulting fromuse of a high resolution anisotropy model shows improved prediction inboth reservoir and the shale section above and below the reservoir.

With reference to FIG. 5, another embodiment of methods according to thepresent disclosure is shown. Similar to the method illustrated in FIG.2, the method of FIG. 5 may begin at step 502 by inverting seismic dataup to conventional far angles (i.e., up to about 40°-45°) usingconventional migration or elastic FWI to infer I_(P) and at least one ofI_(S), V_(P)/V_(S), V_(S)/V_(P), and V_(S). At step 504, aninhomogeneous anisotropy model and an inhomogeneous V_(P)/V_(S) orV_(S)/V_(P) model are constructed, using the methodology of interpretedgeobodies (as in step 204). It should be understood that this stepenvisions constructing the inhomogeneous anisotropy model before, after,or simultaneously with the inhomogeneous V_(P)/V_(S) or V_(S)/V_(P)model. For example, an inhomogeneous anisotropy model may be constructedas described in step 204, and for constructing an inhomogeneousV_(S)/V_(P) model, a thresholding function and/or direct mapping fromseismic stacks and/or previous elastic FWI products I_(P) andV_(S)/V_(P) (produced in step 502) can be used to set areascorresponding to shale at lower V_(S)/V_(P) values and areascorresponding to sand at higher V_(S)/V_(P) values. As with theembodiment illustrated in FIG. 2, step 502 is optional and theinhomogeneous anisotropy and V_(P)/V_(S) or V_(S)/V_(P) models may beconstructed on the basis of seismic facies analysis or regional geologicknowledge alone, for example.

The refined inhomogeneous V_(P)/V_(S) or V_(S)/V_(P) and anisotropymodels are used at step 506 to obtain a third parameter via elastic FWIor simultaneously invert for multiple parameters. For example, thefar-offset range of seismic data may be inverted for p, using an elasticinversion algorithm, with I_(P) and V_(P)/V_(S) fixed. V_(P) may then becomputed from I_(P) using the definition of acoustic impedance and ρ asdetermined in 502. Or the far-offset range may be inverted for V_(P),using an elastic inversion algorithm, with I_(P) and V_(P)/V_(S) fixed.Density ρ may then be computed from I_(P) using the definition ofacoustic impedance and V_(P) as determined may be determined in 502.Persons of ordinary skill in the art will recognize that variations of asequential or simultaneous elastic FWI approach may be performed at step506 while holding the updated V_(P)/V_(S) or V_(S)/V_(P) model fixed.

To illustrate some advantages of the method of FIG. 5, an example isprovided in FIGS. 6A-6F. In particular, FIG. 6A shows an initial(smooth) V_(S)/V_(P) model, and FIG. 6D shows its corresponding invertedV_(S)/V_(P) model. For comparison, FIG. 6B shows an inhomogeneousV_(S)/V_(P) model refined using methodologies described herein. Forsimplicity, in this example the inhomogeneous anisotropy modelconstructed in the previous example (FIG. 3D) was used together with theupdated V_(S)/V_(P) model shown in FIG. 6B to conduct elastic FWI toinvert for V_(S)/V_(P) as shown in FIG. 6E. The “true” V_(S)/V_(P) modelreflecting the effect of geological differences is provided in FIG. 6C,and its inverted counterpart in FIG. 6F. It is evident that the invertedV_(S)/V_(P) model obtained by using inhomogeneous anisotropy andinhomogeneous V_(S)/V_(P) models according to methods described hereinmore closely matches the true answer.

FIG. 7 shows the comparison of V_(S)/V_(P) models and invertedV_(S)/V_(P) models (after detrending) as well-logs. In particular, line702 corresponds to the conventional (unmodified) V_(S)/V_(P) model, line704 to the updated V_(S)/V_(P) model, and line 706 to the “true”V_(S)/V_(P) model. Corresponding inverted V_(S)/V_(P) models afterdetrending 712, 714, and 716 were generated using the conventionalV_(S)/V_(P) model, modified V_(S)/V_(P) model (inhomogeneous) and thetrue V_(S)/V_(P) model, respectively. It can be appreciated that theinverted V_(S)/V_(P) model 712 using the homogeneous V_(S)/V_(P) modelunder-predicts the reservoir V_(S)/V_(P) magnitude and over-predicts theV_(S)/V_(P) magnitude in the shale above and below, curve 716. However,the curve 714, which results from use of a high resolution anisotropyand V_(S)/V_(P) models, shows improved prediction in both reservoir andthe shale section above and below the reservoir. Since FWI works atseismic resolution, the velocity models obtained using elastic FWI havemuch higher resolution than conventional velocity models obtained fromimaging. Improved, high-frequency information about the subsurfacevelocity models is not only useful for kinematic imaging to produceimproved stacks, but it can also bring additional geological insight tohelp with interpretation.

According to some other aspects of the present disclosure, a thirdembodiment is contemplated in which only the background V_(P)/V_(S) orV_(S)/V_(P) model is updated to create an inhomogeneous V_(P)/V_(S) orV_(S)/V_(P) model. Specifically, as shown in FIG. 8, alternative methodsmay begin at step 802 by inverting seismic data up to conventional farangles (i.e., up to about) 40°-45° using conventional migration orelastic FWI to infer I_(P) and at least one of I_(S), V_(P)/V_(S),V_(S)/V_(P), and V_(S). At step 804, an inhomogeneous V_(P)/V_(S) orV_(S)/V_(P) model is constructed using the methodology of interpretedgeobodies (as in step 504). For example, a thresholding function and/ordirect mapping from seismic stacks and/or previous elastic FWI productsI_(P) and V_(S)/V_(P) can be used to set areas corresponding to shale atlower V_(S)/V_(P) values and areas corresponding to sand at higherV_(S)/V_(P) values. The refined inhomogeneous V_(P)/V_(S) or V_(S)/V_(P)model may then be used at step 806 to obtain a third parameter viaelastic FWI or simultaneously invert for multiple parameters.

Updated physical property models may be used to prospect forhydrocarbons or otherwise be used in hydrocarbon management. As usedherein, hydrocarbon management includes hydrocarbon extraction,hydrocarbon production, hydrocarbon exploration, identifying potentialhydrocarbon-bearing formations, characterizing hydrocarbon-bearing toformations, identifying well locations, determining well injectionrates, determining well extraction rates, identifying reservoirconnectivity, acquiring, disposing of and/or abandoning hydrocarbonresources, reviewing prior hydrocarbon management decisions, and anyother hydrocarbon-related acts or activities. For, example, prospectingcan include causing a well to be drilled that targets a hydrocarbondeposit derived from a subsurface image generated from the updatedmodel.

In all practical applications, the present technological advancementmust be used in conjunction with a computer, programmed in accordancewith the disclosures herein. For example, FIG. 9 is a diagram of anexemplary computer system 900 that may be utilized to implement methodsdescribed herein. A central processing unit (CPU) 902 is coupled tosystem bus 904. The CPU 902 may be any general-purpose CPU, althoughother types of architectures of CPU 902 (or other components ofexemplary system 900) may be used as long as CPU 902 (and othercomponents of system 900) supports the operations as described herein.Those of ordinary skill in the art will appreciate that, while only asingle CPU 902 is shown in FIG. 9, additional CPUs may be present.Moreover, the computer system 900 may comprise a networked,multi-processor computer system that may include a hybrid parallelCPU/GPU system. The CPU 902 may execute the various logical instructionsaccording to various teachings disclosed herein. For example, the CPU902 may execute machine-level instructions for performing processingaccording to the operational flow described.

The computer system 900 may also include computer components such asnon-transitory, computer-readable media. Examples of computer-readablemedia include a random access memory (RAM) 906, which may be SRAM, DRAM,SDRAM, or the like. The computer system 900 may also include additionalnon-transitory, computer-readable media such as a read-only memory (ROM)908, which may be PROM, EPROM, EEPROM, or the like. RAM 906 and ROM 908hold user and system data and programs, as is known in the art. Thecomputer system 900 may also include an input/output (I/O) adapter 910,a graphics processing unit (GPU) 914, a communications adapter 922, auser interface adapter 924, a display driver 916, and a display adapter918.

The I/O adapter 910 may connect additional non-transitory,computer-readable media such as a storage device(s) 912, including, forexample, a hard drive, a compact disc (CD) drive, a floppy disk drive, atape drive, and the like to computer system 900. The storage device(s)may be used when RAM 906 is insufficient for the memory requirementsassociated with storing data for operations of the present techniques.The data storage of the computer system 900 may be used for storinginformation and/or other data used or generated as disclosed herein. Forexample, storage device(s) 912 may be used to store configurationinformation or additional plug-ins in accordance with the presenttechniques. Further, user interface adapter 924 couples user inputdevices, such as a keyboard 928, a pointing device 926 and/or outputdevices to the computer system 900. The display adapter 918 is driven bythe CPU 902 to control the display on a display device 920 to, forexample, present information to the user such as subsurface imagesgenerated according to methods described herein.

The architecture of system 900 may be varied as desired. For example,any suitable processor-based device may be used, including withoutlimitation personal computers, laptop computers, computer workstations,and multi-processor servers. Moreover, the present technologicaladvancement may be implemented on application specific integratedcircuits (ASICs) or very large scale integrated (VLSI) circuits. Infact, persons of ordinary skill in the art may use any number ofsuitable hardware structures capable of executing logical operationsaccording to the present technological advancement. The term “processingcircuit” encompasses a hardware processor (such as those found in thehardware devices noted above), ASICs, and VLSI circuits. Input data tothe computer system 900 may include various plug-ins and library files.Input data may additionally include configuration information.

Preferably, the computer is a high performance computer (HPC), known asto those skilled in the art. Such high performance computers typicallyinvolve clusters of nodes, each node having multiple CPU's and computermemory that allow parallel computation. The models may be visualized andedited using any interactive visualization programs and associatedhardware, such as monitors and projectors. The architecture of systemmay vary and may be composed of any number of suitable hardwarestructures capable of executing logical operations and displaying theoutput according to the present technological advancement. Those ofordinary skill in the art are aware of suitable supercomputers availablefrom Cray or IBM.

Disclosed aspects may include any combinations of the methods andsystems shown in the following numbered paragraphs. This is not to beconsidered a complete listing of all possible aspects, as any number ofvariations can be envisioned from the description above.

It should be understood that the numerous changes, modifications, andalternatives to the preceding disclosure can be made without departingfrom the scope of the disclosure. The preceding description, therefore,is not meant to limit the scope of the disclosure. Rather, the scope ofthe disclosure is to be determined only by the appended claims and theirequivalents. It is also contemplated that structures and features in thepresent examples can be altered, rearranged, substituted, deleted,duplicated, combined, or added to each other.

REFERENCES

The following references are incorporated herein in their entirety inall jurisdictions that allow it:

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What is claimed is:
 1. A computer-implemented method for inversion ofseismic data to infer subsurface physical property parameterscomprising: constructing an inhomogeneous anisotropy model; andinverting the seismic data in a sequential or simultaneous approach toobtain at least one subsurface physical property parameter using anelastic inversion algorithm and the inhomogeneous anisotropy model;wherein the subsurface physical property parameters comprise P-wavevelocity V_(P), S-u) wave velocity V_(S), density, lambda, mu, andcombinations thereof.
 2. The method of claim 1, wherein using an elasticinversion algorithm comprises: extracting only PP mode data from theseismic data; inverting the PP mode data sequentially in two or moredifferent offset ranges, each offset range inversion determining P-waveimpedance (I_(P)) and at least one of S-wave impedance (I_(S)), P-wavevelocity over S-wave velocity (V_(P)/V_(S)), S-wave velocity over P-wavevelocity (V_(S)/V_(P)), and S-wave velocity (V_(S)), wherein in a secondand subsequent inversions, parameters determined in a previous inversionare held fixed; and using the inverted subsurface physical propertyparameters to construct the inhomogeneous anisotropy model.
 3. Themethod of claim 2, wherein a near-offset range is sequentially first tobe inverted to infer I_(P), using a computer programmed with an acousticor elastic inversion algorithm.
 4. The method of claim 3, wherein amid-offset range is sequentially second to be inverted to infer at leastone of I_(S), V_(P)/V_(S), V_(S)/V_(P), and V_(S), with I_(P) fixed atits value from the first inversion, said second inversion using anelastic inversion algorithm.
 5. The method of claim 4, wherein invertingthe seismic data is performed in a sequential approach comprising:inverting a far-offset range to infer density or V_(P), using an elasticinversion algorithm, with I_(P) fixed at its value from the inversion ofthe near-offset range and I_(P) or V_(P)/V_(S) or V_(S)/V_(P) or V_(S)fixed at its value from the inversion of the mid-offset range.
 6. Themethod of claim 5, wherein density is inferred, and further comprising:computing V_(P) from the relationship I_(P)=ρV_(P) using I_(P) and theinferred density.
 7. The method of claim 5, wherein V_(P) is inferred,and further comprising: computing density from the relationshipI_(P)=ρV_(P) using I_(P) and the inferred V_(P).
 8. The method of claim5, further comprising repeating the inversions of the near-offset data,mid-offset data, and far-offset data at least one time to update theinferred physical property parameters.
 9. The method of claim 4, whereinthe acoustic and elastic inversion algorithms are full waveforminversion algorithms.
 10. The method of claim 1, wherein constructingthe inhomogeneous anisotropy model comprises: deriving geobodies from atleast one of seismic facies analysis, regional geologic information, orseismically derived earth models; and adjusting at least one of ε, δ, γ,or parameters of the elastic stiffness tensor matrix in a homogeneousanisotropy model in areas corresponding to the geobodies.
 11. The methodof claim 10, wherein the geobodies are sand geobodies, and ε and δ areadjusted to be less than or equal to zero.
 12. A computer-implementedmethod for inversion of seismic data to infer subsurface physicalproperty parameters comprising: constructing an inhomogeneous anisotropymodel and an inhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model; andinverting the seismic data in a sequential or simultaneous approach toobtain at least one subsurface physical property parameter using anelastic inversion algorithm and the inhomogeneous anisotropy model andthe inhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model; wherein thesubsurface physical property parameters comprise P-wave velocity V_(P),S-wave velocity V_(S), density, lambda, mu, and combinations thereof.13. The method of claim 12, wherein using an elastic inversion algorithmcomprises: extracting only PP mode data from the seismic data; invertingthe PP mode data sequentially in two or more different offset ranges,each offset range inversion determining P-wave impedance (I_(P)) and atleast one of S-wave impedance (I_(S)), P-wave velocity over S-wavevelocity (V_(P)/V_(S)), S-wave velocity over P-wave velocity(V_(S)/V_(P)), and S-wave velocity (V_(S)), wherein in a second andsubsequent inversions, parameters determined in a previous inversion areheld fixed; and using the inverted subsurface physical propertyparameters to construct the inhomogeneous anisotropy model and theinhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model.
 14. The method of claim13, wherein a near-offset range is sequentially first to be inverted toinfer I_(P), using a computer programmed with an acoustic or elasticinversion algorithm.
 15. The method of claim 14, wherein a mid-offsetrange is sequentially second to be inverted to infer at least one ofI_(S), V_(P)/V_(S), V_(S)/V_(P), and V_(S), with I_(P) fixed at itsvalue from the first inversion, said second inversion using an elasticinversion algorithm.
 16. The method of claim 15, wherein inverting theseismic data is performed in a sequential approach comprising: invertinga far-offset range to infer density or V_(P), using an elastic inversionalgorithm, with I_(P) fixed at its value from the inversion of thenear-offset range and I_(P) or V_(P)/V_(S) or V_(S)/V_(P) or V_(S) fixedat its value from the inversion of the mid-offset range.
 17. The methodof claim 16, wherein density is inferred, and further comprising:computing V_(P) from the relationship I_(P)=ρV_(P) using I_(P) and theinferred density.
 18. The method of claim 16, wherein V_(P) is inferred,and further comprising: computing density from the relationshipI_(P)=ρV_(P) using I_(P) and the inferred V_(P).
 19. The method of claim16, further comprising repeating the inversions of the near-offset data,mid-offset data, and far-offset data at least one time to update theinferred physical property parameters.
 20. The method of claim 15,wherein the acoustic and elastic inversion algorithms are full waveforminversion algorithms.
 21. The method of claim 12, wherein constructingthe inhomogeneous anisotropy model comprises: deriving geobodies from atleast one of seismic facies analysis, regional geologic information, orseismically derived earth models; and adjusting at least one of ε, δ, γ,or parameters of the elastic stiffness tensor matrix in a homogeneousanisotropy model in areas corresponding to the geobodies.
 22. The methodof claim 21, wherein the geobodies are sand geobodies, and ε and δ areadjusted to be less than or equal to zero.
 23. The method of claim 12,wherein constructing the inhomogeneous V_(S)/V_(P) or V_(P)/V_(S) tomodel comprises: deriving geobodies from at least one of seismic faciesanalysis, regional geologic information, or seismically derived earthmodels; and adjusting values in a homogeneous V_(S)/V_(P) or V_(P)/V_(S)model in areas corresponding to the geobodies.
 24. The method of claim23, wherein the geobodies are sand geobodies, and areas corresponding tosand are assigned lower V_(P)/V_(S) values if constructing a V_(P)/V_(S)model or assigned higher V_(S)/V_(P) values if constructing aV_(S)/V_(P) model.
 25. A computer-implemented method for inversion ofseismic data to infer subsurface physical property parameterscomprising: constructing an inhomogeneous V_(S)/V_(P) or V_(P)/V_(S)model; and inverting the seismic data in a sequential or simultaneousapproach to obtain at least one subsurface physical property parameterusing an elastic inversion algorithm and the inhomogeneous V_(S)/V_(P)or V_(P)/V_(S) model; wherein the subsurface physical propertyparameters comprise P-wave velocity V_(P), S-wave velocity V_(S),density, lambda, mu, and combinations thereof.
 26. The method of claim25, wherein using an elastic inversion algorithm comprises: extractingonly PP mode data from the seismic data; inverting the PP mode datasequentially in two or more different offset ranges, each offset rangeinversion determining P-wave impedance (I_(P)) and at least one ofS-wave impedance (I_(S)), P-wave velocity over S-wave velocity(V_(P)V_(S)), S-wave velocity over P-wave velocity (V_(S)/V_(P)), andS-wave velocity (V_(S)), wherein in a second and subsequent inversions,parameters determined in a previous inversion are held fixed; and usingthe inverted subsurface physical property parameters to construct theinhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model.
 27. The method of claim26, wherein a near-offset range is sequentially first to be inverted toinfer I_(P), using a computer programmed with an acoustic or elasticinversion algorithm.
 28. The method of claim 27, wherein a mid-offsetrange is sequentially second to be inverted to infer at least one ofI_(S), V_(P)/V_(S), V_(S)/V_(P), and V_(S), with I_(P) fixed at itsvalue from the first inversion, said second inversion using an elasticinversion algorithm.
 29. The method of claim 28, wherein inverting theseismic data is performed in a sequential approach comprising: invertinga far-offset range to infer density or V_(P), using an elastic inversionalgorithm, with I_(P) fixed at its value from the inversion of thenear-offset range and I_(P) or V_(P)/V_(S) or V_(S)/V_(P) or V_(S) fixedat its value from the inversion of the mid-offset range.
 30. The methodof claim 29, wherein density is inferred, and further comprising:computing V_(P) from the relationship I_(P)=ρV_(P) using I_(P) and theinferred density.
 31. The method of claim 29, wherein V_(P) is inferred,and further comprising: computing density from the relationshipI_(P)=ρV_(P) using I_(P) and the inferred V_(P).
 32. The method of claim29, further comprising repeating the inversions of the near-offset data,mid-offset data, and far-offset data at least one time to update theinferred physical property parameters.
 33. The method of claim 28,wherein the acoustic and elastic inversion algorithms are full waveforminversion algorithms.
 34. The method of claim 25, wherein constructingthe inhomogeneous V_(S)/V_(P) or V_(P)/V_(S) model comprises: derivinggeobodies from at least one of seismic facies analysis, regionalgeologic information, or seismically derived earth models; and adjustingvalues in a homogeneous V_(S)/V_(P) or V_(P)/V_(S) model in areascorresponding to the geobodies.
 35. The method of claim 34, wherein thegeobodies are sand geobodies, and areas corresponding to sand areassigned lower V_(P)/V_(S) values if constructing a V_(P)/V_(S) model orassigned higher V_(S)/V_(P) values if constructing a V_(S)/V_(P) model.